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Since amount of electrons in another isotope is the same the J stays the same for both isotopes so you know J. We know I and we can measure a with a = mu B_J/IJ. The unknowns here are B_J and mu. Since you have all the data for the original isotope (with I_1 and mu_1) you can calculate B_J, this is the same B_J as for isotope 2 (electrons stay the same for different isotopes). Now you have all parameters in a to calculate mu, mu= aIJ/B_J. With B_J calculated from the original isotope, J from the original isotope, I known and a measured.
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